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Combinatorial Methods in Density Estimation

  • Luc Devroye
  • Gábor Lugosi

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Luc Devroye, Gábor Lugosi
    Pages 1-3
  3. Luc Devroye, Gábor Lugosi
    Pages 4-16
  4. Luc Devroye, Gábor Lugosi
    Pages 17-26
  5. Luc Devroye, Gábor Lugosi
    Pages 27-37
  6. Luc Devroye, Gábor Lugosi
    Pages 38-46
  7. Luc Devroye, Gábor Lugosi
    Pages 47-57
  8. Luc Devroye, Gábor Lugosi
    Pages 58-69
  9. Luc Devroye, Gábor Lugosi
    Pages 70-78
  10. Luc Devroye, Gábor Lugosi
    Pages 79-97
  11. Luc Devroye, Gábor Lugosi
    Pages 98-107
  12. Luc Devroye, Gábor Lugosi
    Pages 108-117
  13. Luc Devroye, Gábor Lugosi
    Pages 118-133
  14. Luc Devroye, Gábor Lugosi
    Pages 134-141
  15. Luc Devroye, Gábor Lugosi
    Pages 142-149
  16. Luc Devroye, Gábor Lugosi
    Pages 150-176
  17. Luc Devroye, Gábor Lugosi
    Pages 177-189
  18. Luc Devroye, Gábor Lugosi
    Pages 190-197
  19. Back Matter
    Pages 199-209

About this book

Introduction

Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.

Keywords

Density Estimation Likelihood Maxima Probability theory Variance

Authors and affiliations

  • Luc Devroye
    • 1
  • Gábor Lugosi
    • 2
  1. 1.Computer Science DepartmentMcGill UniversityMontrealCanada
  2. 2.Facultat de Ciencies EconomiquesUniversitat Pompeu FabraBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0125-7
  • Copyright Information Springer-Verlag New York, Inc. 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6527-6
  • Online ISBN 978-1-4613-0125-7
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site